W. Rühaak

Finite element modeling of borehole heat exchanger systems

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. The first part of the paper derives the fundamental equations for BHE systems and their finite element representations, where the thermal exchange between the borehole components is modeled via thermal transfer relations. For this purpose improved relationships for thermal resistances and capacities of BHE are introduced. Pipe-to-grout thermal transfer possesses multiple grout points for double U-shape and single U-shape BHE to attain a more accurate modeling. The numerical solution of the final 3D problems is performed via a widely non-sequential (essentially non-iterative) coupling strategy for the BHE and porous medium discretization. Four types of vertical BHE are supported: double U-shape (2U) pipe, single U-shape (1U) pipe, coaxial pipe with annular (CXA) and centred (CXC) inlet. Two computational strategies are used: (1) The analytical BHE method based on Eskilson and Claessons (1988) solution, (2) numerical BHE method based on Al-Khoury et al.s (2005) solution. The second part of the paper focusses on BHE meshing aspects, the validation of BHE solutions and practical applications for borehole thermal energy store systems.

Finite element modeling of borehole heat exchanger systems: Part 2. Numerical simulation

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. Applying BHE in regional discretizations optimal conditions of mesh spacing around singular BHE nodes are derived. Optimal meshes have shown superior to such discretizations which are either too fine or too coarse. The numerical methods are benchmarked against analytical and numerical reference solutions. Practical application to a borehole thermal energy store (BTES) consisting of 80 BHE is given for the real-site BTES Crailsheim, Germany. The simulations are controlled by the specifically developed FEFLOW-TRNSYS coupling module. Scenarios indicate the effect of the groundwater flow regime on efficiency and reliability of the subsurface heat storage system.

On the impact of explicitly predicted runoff on the simulated atmospheric response to small-scale land-use changes—an integrated modeling approach

Abstract An integrated modeling approach was developed to simulate the water cycle in a closed manner. It consists of (1) procedures for up- and downscaling of the variables and fluxes important for both the hydrological and atmospheric processes, (2) a module to explicitly predict surface and channel runoff, (3) the hydro-thermodynamic soil–vegetation scheme (HTSVS) which was introduced in the (4) nonhydrostatic meso-β/γ-scale meteorological model GESIMA (Geesthachts simulation model of the atmosphere). Comparison of the results provided by simulations with and without consideration of surface and channel runoff shows a remarkable impact of surface runoff on the water cycle within the domain. The results of simulations, wherein, along the rivers, grassland and agriculturally used land were substituted by deciduous forest demonstrate that the atmospheric response to land-use changes is more distinct when surface runoff is considered explicitly than if not. It can be concluded that an integrated modeling techniques of the water cycle, like presented here, can be an important tool for studies on water availability under altered future conditions.

A Java application for quality weighted 3-d interpolation

iw3d is a tool for 3-d interpolation of scattered data. The program is endowed with a user-friendly graphical interface. The interpolation-algorithm is a modified version of the inverse-distance weighting method. It has the capability for a quality-weighted interpolation. The interpolation can be carried out with a sector-search approach for reducing clustering effects. A semivariogram is calculated for the three cartesian main directions to give an estimate for a selectable search-distance. Tests of the program with a synthetic 3-d data set and a large set of measured subsurface temperatures with different qualities show good results. iw3d is programmed with Java (TM) and is a GPL licensed open source. It has been successfully tested with different Java versions on Microsoft Windows, Sun Solaris and on several Linux distributions. The current version is available at http://geomath.onlinehome.de/iw3d/.

Processing of rock core microtomography images

The abilities of machine learning algorithms to process X-ray microtomographic rock images were determined. The study focused on the use of unsupervised, supervised, and ensemble clustering techniques, to segment X-ray computer microtomography rock images and to estimate the pore spaces and pore size diameters in the rocks. The unsupervised k-means technique gave the fastest processing time and the supervised least squares support vector machine technique gave the slowest processing time. Multiphase assemblages of solid phases (minerals and finely grained minerals) and the pore phase were found on visual inspection of the images. In general, the accuracy in terms of porosity values and pore size distribution was found to be strongly affected by the feature vectors selected. Relative porosity average value of 15.92?1.77% retrieved from all the seven machine learning algorithm is in very good agreement with the experimental results of 17?2%, obtained using gas pycnometer. Of the supervised techniques, the least square support vector machine technique is superior to feed forward artificial neural network because of its ability to identify a generalized pattern. In the ensemble classification techniques boosting technique converged faster compared to bragging technique. The k-means technique outperformed the fuzzy c-means and self-organized maps techniques in terms of accuracy and speed. Testing of machine learning algorithms to process X-ray CT rock images.Unsupervised, supervised, and ensemble clustering techniques were applied.k-Means technique is the fastest in terms of CPU performance.

3-D interpolation of subsurface temperature data with measurement error using kriging

A computer program called jk3d for 3-D ordinary kriging interpolation of scattered data has been developed. A specific feature of the code is that differences of the quality of the measured data are taken into account by weighting them according to the assumed error of the data. The code is demonstrated on subsurface temperature measurements with different measurement errors. One of the main problems when ordinary kriging is used for 3-D subsurface data is a lack of sufficient data for computing the necessary variograms. A feasible procedure to obtain such a variogram is discussed. The final result of the 3-D interpolated temperature data shows, that the quality of the interpolation increases substantially if the measurement error is taken into account. The code uses a modified GSLIB like input. Although not all functions of the GSLIB kriging library are supported, all substantial functions are available. jk3d is LGPL licensed, open source. The current version is available at http://sourceforge.net/projects/jk3d.html.

3D hydro-mechanically coupled groundwater flow modelling of Pleistocene glaciation effects

Pleistocene glaciation led to temporal and spatial variations of sub-surface pore fluid pressure. In basins covered by ice sheets, fluid flow and recharge rates are strongly elevated during glaciations as compared to inter-glacial periods. Present-day hydrogeological conditions across formerly glaciated areas are likely to still reflect the impact of glaciations that ended locally more than 10 thousand years before present.3D hydro-mechanical coupled modelling of glaciation can help to improve the management of groundwater resources in formerly glaciated basins.An open source numerical code for solving linear elasticity, which is based on the finite element method (FEM) in 3D, has been developed. By coupling this code with existing 3D flow codes it is possible to enable hydro-mechanical coupled modelling.Results of two benchmark simulations are compared to existing analytical solutions to demonstrate the performance of the newly developed code. While the result for a fluid-structure coupled case is in reasonable agreement with the analytical model, the result for a classical structure-fluid coupled benchmark showed that the analytical solution only matches the numerical result when the relevant coupling parameter (loading efficiency) is known in advance. This indicates that the applicability of widely applied approaches using an extra term in the groundwater flow equation for vertical stress to simulate hydro-mechanical coupling might have to be re-evaluated.A case study with the commercial groundwater simulator FEFLOW demonstrates the newly developed solution. Pleistocene glaciation has led to variations of the sub-surface pore fluid pressure.A code for 3D hydro-mechanical modelling was developed to study such phenomena.The code has been verified using different benchmarks.Application is demonstrated for a 3D case of temporal and spatial variable glaciations.

Thermo-Triax: An Apparatus for Testing Petrophysical Properties of Rocks Under Simulated Geothermal Reservoir Conditions

A Thermo-Triax apparatus has been developed to facilitate research on petrophysical properties of rock samples under simulated geothermal reservoir conditions. The apparatus consists of control systems for vertical stress and horizontal confining pressure, a pair of independent pore pressure controllers for applying different upstream, and downstream pore pressures at bottom and top of rock specimens, an external heater and a data logging system. Permeability of rocks is measured using steady state and transient flow methods. The thermal expansion of metallic parts in the triaxial cell and the error introduced into the readings of the extensometers at high temperatures are calibrated via experiments on an aluminum specimen with known coefficient of thermal expansion. The possibilities of studying the effect of stress and temperature on permeability and compressibilities of porous rocks with the Thermo-Triax apparatus are presented with first data. The change of pore volume during the non-isothermal process between adjacent temperature levels as well as along the measurement of permeability at leveled temperatures is interpreted and calibrated. The thermal expansion of mineral grains during heating is verified with the data of pore volume change and the magnitude of thermal expansion of mineral grains is estimated and compared with reported values. The permeability measurements along different heating paths can be used to verify the temperature dependency of stress-dependent rock properties.

Geostatistical Interpolation of Subsurface Properties by Combining Measurements and Models

Subsurface temperature is the key parameter in geothermal exploration. An accurate estimation of the reservoir temperature is of high importance and usually done either by interpolation of borehole temperature measurement data or numerical modeling. However, temperature measurements at depths which are of interest for deep geothermal applications (usually deeper than 2 km) are generally sparse. A pure interpolation of such sparse data always involves large uncertainties and usually neglects knowledge of the 3D reservoir geometry or the rock and reservoir properties governing the heat transport. Classical numerical modeling approaches at regional scale usually only include conductive heat transport and do not reflect thermal anomalies along faults created by convective transport. These thermal anomalies however are usually the target of geothermal exploitation. Kriging with trend does allow including secondary data to improve the interpolation of the primary one. Using this approach temperature measurements of depths larger than 1,000 m of the federal state of Hessen/Germany have been interpolated in 3D. A 3D numerical conductive temperature model was used as secondary information. This way the interpolation result reflects thermal anomalies detected by direct temperature measurements as well as the geological structure. This results in a considerable quality increase of the subsurface temperature estimation.

Prognosefähigkeit numerischer Erdwärmesondenmodelle

ZusammenfassungFür größere Erdwärmesondenanlagen werden standardmäßig numerische Berechnungen durchgeführt. Anlass sind neben der Dimensionierung (Bestimmung von Anzahl und Tiefe der benötigten Erdwärmesonden) vor allem genehmigungsrechtliche Fragestellungen, bei denen häufig eine möglichst realistische Modellierung gefordert wird.Eine solche realistische Simulation ist technisch durchführbar, jedoch sehr aufwändig. Ein wichtiger Aspekt, der dabei in den Hintergrund gerät, ist die Quantifizierung der Parameterunsicherheiten aufgrund der natürlichen Heterogenität des geologischen Untergrundes.Statt nur eine einzelne möglichst realistische Prognoseberechnung durchzuführen, kann die zusätzliche Berechnung von Ensemblemodellen, das heißt einer höheren Anzahl von sinnvoll vereinfachten Modellen, oftmals hilfreich sein. Durch Variation der Untergrundkennwerte im Bereich der vermuteten Unsicherheiten können Prognoseunsicherheiten bestimmt und dem Planer sowie dem Gutachter damit wichtige Zusatzinformationen zur Verfügung gestellt werden.AbstractLarge installations of borehole heat exchangers (BHEs) typically require numerical modeling. A reasonable system dimensioning (number and depth of BHEs) has to be found and regulatory requirements (minimizing environmental impact and avoiding competitive usage) have to be met. In the latter case, highly realistic models are typically demanded. Such realistic models are technically possible, but very laborious. One important issue, which is often neglected, is the quantification of parameter uncertainties due to heterogeneity of the geological subsurface.Instead of a single forecast model, the additional computation of so-called ensemble models, i.e. a larger number of more simplified models, should be considered. By varying the relevant characteristics of the subsurface within the range of uncertainty, the quality of the forecast can be estimated, and the system designer can obtain valuable additional information.